$B_s^0 \to η^{(\prime)} η^{(\prime)}$ decays in the pQCD approach

Abstract

We calculate the CP averaged branching ratios and CP-violating asymmetries for $B_s^0 \to ηη, ηη^\prime$ and $η^\prime η^\prime$ decays in the perturbative QCD (pQCD) approach here. The pQCD predictions for the CP-averaged branching ratios are $Br(B_s^0 \to ηη) = \left (14.2^{+18.0}_{-7.5}) \times 10^{-6}$, $Br(B_s^0 \to ηη^\prime)= \left (12.4 ^{+18.2}_{-7.0}) \times 10^{-6}$, and $Br(B_s^0 \to η^{\prime} η^{\prime}) = \left (9.2^{+15.3}_{-4.9}) \times 10^{-6}$, which agree well with those obtained by employing the QCD factorization approach and also be consistent with available experimental upper limits. The gluonic contributions are small in size: less than 7% for $B_s \to ηη$ and $ ηη^\prime$ decays, and around 18% for $B_s \to η' η'$ decay. The CP-violating asymmetries for three decays are very small: less than 3% in magnitude.